Chapter 4 Development of a New Model
Electrons behave like particles in some experiments, and like waves in others. The electron's 'wave/particle duality' has no real analogy in the everyday world. The quantum theory that describes the behavior of electrons is a cornerstone in modern chemistry. Quantum theory can be used to explain: why atoms are stable, why things have the color they do, why the periodic table has the structure it does, why chemical bonds form, why different elements combine in different ratios with each other.
Properties of Light Light and electrons both behave quantum mechanically. Waves Waves are an oscillation that moves outward from a disturbance (ripples moving away from a pebble dropped into a pond)
Properties of waves property definition symbol SI unit velocity amplitude wavelength frequency distance traveled per second peak height above midline peak-to-peak distance number of peaks passing by per second c A Lambda nu m/s varies with type of wave m s -1 (called Hertz)
relationship between frequency and wavelength distance per cycle cycles per second = distance per second = c examples C= The speed of sound in air is 330 m/s. Humans can hear sounds with wavelengths between 17 m and 17 mm. What is the highest sound frequency that is audible?
interference constructive interference: amplitudes add peaks, troughs of interfering waves occur in the same positions (waves are in phase ) destructive interference: amplitudes cancel peaks of one wave are in same position as troughs of the other (waves are out of phase )
Diffraction The ability of a wave to bend around the edges of obstacles or holes. The effect is most noticeable when the obstacle or hole is comparable to the size of the wavelength Waves can bend around small obstacles and fan out from pinholes. particles effuse from pinholes.
a wave can't bend around obstacles much larger than its wavelength what does this imply about the wavelength of sound waves? radio waves? visible light? waves are delocalized (spread out in space) wave behavior waves interfere waves diffract waves are delocalized particle behavior particles collide particles effuse particles are localized
Is light a stream of particles or a wave? Thomas Young, 1801 pass light through two tiny adjacent slits if light were particles: target would be brightest where light passing through the slits overlapped target would darken steadily moving away from the overlap region this was not observed! a pattern of light and dark stripes was observed instead Young explained the stripes as a combination of diffraction and interference these interference fringes are a sure sign of wave behavior White areas are peak-peak or trough-trough overlaps (constructive interference) black areas are peak-trough overlaps (destructive interference).
Force Fields force field: a region where forces act on an object; strength of forces vary with position gravitational fields larger mass at center of field = stronger forces larger distance from center of field = weaker forces electric fields opposite charges attract each other, but like charges repel each other larger charge at center of field = stronger forces larger distance from center of field = weaker forces magnetic fields can be produced by moving charges (electromagnets) a moving magnetic field can produce an electric field (electric generator)
Electromagnetic radiation James Clerk Maxwell ca. 1855 changes in electric and magnetic fields are always coupled: electromagnetism making e/m waves with a vibrating charge both electric and magnetic fields oscillate oscillations are at right angles electric oscillation produces magnetic oscillation, which produces another electric oscillation, and on and on vibrating charge creates a ripple in the electromagnetic field The speed of electromagnetic radiation was computed to be around 3 10 8 m/s The same speed had been determined experimentally for light! hypothesis: light is a form of electromagnetic radiation (Maxwell, 1862)
Electromagnetic spectrum
Energy of electromagnetic radiation radiation carries energy through space work is done on charges in the e/m field transmitter loses energy; receiver gains energy higher amplitude means higher energy per peak amplitude squared determines the intensity or brightness of light therefore, brighter light should carry more energy per peak than dimmer light
Max Planck Did an experiment to measure the energy carried by an electromagnetic wave photoelectric effect: shining light on alkali metals knocks electrons out of metal strategy: measure kinetic energy of ejected electrons; then measure light energy per ejected electron. surprise: brightness has NO EFFECT on the kinetic energy per ejected electron brighter light ejects MORE electrons. surprise #2: red light can't eject any electrons, but blue light can! below a threshold frequency, there are no ejected electrons! frequency is a property of the metal being used
Planck s mathematical equation Quantum (energy)= minimum quantity of energy that can be lost or gained by an atom Energy = planck s constant x frequency E=h h=6.626 e-34 js
Albert Einstein Albert Einstein's interpretion of the photoelectric effect (Nobel Prize, 1921) maybe light is like a stream of massless particles (call them photons) brighter light has more photons, but bluer light has higher energy photons Changed Planck s work to: Ephoton=h
examples What is the energy of a photon of red light with wavelength 700 nm? What is the wavelength of a photon which has an energy of 1 10-18 J? Shining light of 400 nm on a metal causes electrons with a kinetic energy of 5 10 19 J to be ejected. What is the minimum energy required to eject an electron from the metal? summary: light moves like a wave, but transfers energy like a stream of particles; the particles (photons) have energy equal to h.
The collapsing atom paradox what's the electron doing in an atom? electrons within the atom can't be stationary: positively charged nucleus will attract the negatively charged electron electron will accelerate towards the nucleus if electrons within the atom move, moving charges emit electromagnetic radiation emission will cause electrons to lose energy and spiral into the nucleus the atom will collapse! why don't atoms collapse? classical physics has no answer! key: electrons have wave/particle duality
Electrons as Waves the de Broglie hypothesis (Nobel Prize, 1929) connect wave and particle nature of matter using a relationship that applies to photons: = h/p where p is the momentum of the particle (p = mass times velocity). experimental evidence of electron wave/particle duality electron diffraction C. J. Davisson and G. P. Thomson observed interference fringes when electron beams hit crystal surfaces and thin metal films (Nobel Prize, 1937)
Quantum Model of Atom Louis debroglie Electrons considered waves confined to the space around an atomic nucleus Electrons can exist only at specific frequencies Electrons have wave like properties Created equation that demonstrates---anything that has mass and volume has wavelength
Werner Heisenberg E- detected by their interaction with photons Photons have the same energy as e-, any attempt to locate a specific e- with a photon will knock the e- off course Created Heisenberg uncertainty principle it is impossible to determine simultaneously both the position and velocity of an e- or any other particle.
Erwin Schrodinger Used quantization of e- energies in equation, e- dual wave particle Quantum theory was derived by using Heisenberg Uncertainty Principle and Schrodinger wave equation E- are in orbitals (3-D)
Quantum Numbers Defn.: numbers that specify the properties of atomic orbitals and the properties of e- in orbitals There are 4 Principal Quantum number Symbol n Main energy level occupied by an e- (currently no more than 7)
Angular Momentum number Symbol l Indicates the shape S (sphere) P(peanut) D(dumbell) F (flower)
Magnetic quantum number Symbol m Orientation of an orbital S : 1 orbital P : 3 orbital D: 5 orbital F: 7 orbital Spin quantum number Symbol +1/2 or -1/2 Indicates the two fundamental spins of the e-
Electron Configuration Notation, Orbital Notations, Electron-dot notations Arrangement of e- using 4 quantum numbers Atoms of each element have distinctive electron configurations Atoms electrons tend to assume arrangements that have the lowest possible energies Rules governing: Aufbau principle States an electron occupies the lowest energy orbital that can receive it
Hund s Rule States orbitals of equal energy are each occupied by one electron before any one orbital is occupied by a second electron. All electrons in a singly occupied orbitals must have same spin. Pauli Exclusion Principle States no two electrons in the same atom can have the same set of four quantum numbers Two values of spin quantum number permit two electrons of opposite spins to occupy the same orbital
Each block contains a number of columns equal to the number of electrons that can occupy that subshell The s-block has 2 columns, because a maximum of 2 electrons can occupy the single orbital in an s-subshell. The p-block has 6 columns, because a maximum of 6 electrons can occupy the three orbitals in a p-subshell. The d-block has 10 columns, because a maximum of 10 electrons can occupy the five orbitals in a d-subshell. The f-block has 14 columns, because a maximum of 14 electrons can occupy the seven orbitals in a f-subshell.
Do orbital notation, electron-configuration notation, Nobel-Gas Notation and electron dot notation for each of the following: Rows 1, 3, 5 Do these Chlorine Terbium Iron Silver Iodine Rows 2 and 4 Do these Krypton Phosphorus Cerium Aluminum Lead